Context. Ultra-short-period (USP) planets are defined as planets with orbital periods shorter than one day. This type of planets is rare, highly irradiated, and interesting because their formation history is unknown. Aims. We aim to obtain precise mass and radius measurements to confirm the planetary nature of a USP candidate found by the Transiting Exoplanet Survey Satellite (TESS). These parameters can provide insights into the bulk composition of the planet candidate and help to place constraints on its formation history. Methods. We used TESS light curves and HARPS-N spectrograph radial velocity measurements to establish the physical properties of the transiting exoplanet candidate found around the star HD 20329 (TOI-4524). We performed a joint fit of the light curves and radial velocity time series to measure the mass, radius, and orbital parameters of the candidate. Results. We confirm and characterize HD 20329b, a USP planet transiting a solar-type star. The host star (HD 20329, V = 8.74 mag, J = 7.5 mag) is characterized by its G5 spectral type with M-? = 0.90 +/- 0.05 M-?, R-? = 1.13 +/- 0.02 R-?, and T-eff = 5596 +/- 50 K; it is located at a distance d = 63.68 +/- 0.29 pc. By jointly fitting the available TESS transit light curves and follow-up radial velocity measurements, we find an orbital period of 0.9261 +/- (0.5 x 10(-4)) days, a planetary radius of 1.72 +/- 0.07 R circle plus, and a mass of 7.42 +/- 1.09 M-circle plus, implying a mean density of rho(p) = 8.06 +/- 1.53 g cm(-3). HD 20329b joins the similar to 30 currently known USP planets with radius and Doppler mass measurements.